I'm using a commercial CFD package to solve airflow and heat transfer problems primarily in the areas of electronic cooling and duct design.

Are there any resources or books out there that talk about the required number of nodes/elements/grids versus solution accuracy? Are there any rules of thumb?

I realize that I should be running each problem with several different grid refinements to get a grid independent solution. Unfortunately, my design cycle is too short for that... I'm trying to convince my management that CFD is a good thing for our company... maybe after it's proven, I can ask for more time.

(1). It is important to know what you are going to get out of this CFD exercise. (2). It can be simply that with this CFD exercise your company has raised the technology to a higher level. This alone can be very important in terms of the company's management vision, which in turn can be very valuable. (3). At that level, the ability to run the code successfuly in-house is good enough. (you need to know how to use it though) (4). If your company is in the position to improve the product design, then, you can use the code to do some kind of parametric study and optimization. ( this approach should be more reliable than simple guessing I think) So, at this level, as long as you can obtain reliable trend from the code to guide your design,I think it is better than doing nothing. But you do need to establish this trend first. ( this is the place where you determine the minimum number of mesh points required.) So, it is up to you to say whether it is good enough to use NxMxL mesh size in your design analysis, especially in the case where doubling the mesh points can only give you 10% in return of accuracy. (5). If your goal of doing this CFD exercise is to publish a technical paper in international journals, then, you probably don't have much choice but to look for grid independent solution first. (6). If your goal is to predict accurately the surface heat transfer coefficient, then it is going to be a long war for you. (7). My suggestion is: try to make use of the information you can obtain from the CFD exercise, whether it is the overall mass flow, the flow pattern, the nature of flow separation, the local flow field, the temperature field, etc.. to GUIDE YOUR DESIGN. (8). But if it is faster and cheaper to obtain the similar information using other mathods ( say experimental methods), then I guess, there is no need to do the CFD exercise because other companies are doing it.